Extension of the EMMS Model to Gas-Liquid Systems

Abstract

The Dual-Bubble-Size (DBS) model is an extension of the energy minimization multiscale (EMMS) approach for gas-liquid systems. The system is resolved into a liquid phase, small bubbles and large bubbles, and is jointly dominated by two movement tendencies; i.e., those of the small and large bubbles. A stability condition is formulated to reflect the compromise between these dominant mechanisms, offering another constraint in addition to mass and momentum conservation equations. The DBS model can theoretically predict the regime transition in bubble columns and physically explain the macro-scale evolution of flow structures through the jump change in the global minimum of the micro-scale energy dissipation changing from one point to another within the model space of the structure parameters. The DBS model is found to be an intrinsic model for gas-liquid systems in contrast to the models for single, triple, and multiple classes of bubble. A new model for the ratio of drag coefficient to bubble diameter, that is, the EMMS drag, is then integrated into the Eulerian-Eulerian computational fluid dynamics (CFD) models. The resulting improved prediction demonstrates the ability of the DBS model to reveal the multiscale nature and complexity of gas-liquid systems.